Abstract

Nanomedicine offers the prospect of powerful
new tools for the treatment of human diseases and the
improvement of human biological systems using molecular
nanotechnology. This paper presents a theoretical nanorobot
scaling study for artificial mechanical phagocytes of
microscopic size, called "microbivores,"
whose primary function is to destroy microbiological pathogens
found in the human bloodstream using a digest and discharge
protocol. The
microbivore is an oblate spheroidal nanomedical device
measuring 3.4 microns in diameter along its major axis and 2.0
microns in diameter along its minor axis, consisting of 610
billion precisely arranged structural atoms in a gross geometric
volume of 12.1 micron3. The device may consume up to
200 pW of continuous power while completely digesting trapped
microbes at a maximum throughput of 2 micron3 of
organic material per 30-second cycle. Microbivores are up to
~1000 times faster-acting than either natural or
antibiotic-assisted biological phagocytic defenses, and are ~80
times more efficient as phagocytic agents than macrophages, in
terms of volume/sec digested per unit volume of phagocytic
agent.

1. Introduction

Nanomedicine
[1,
LINK;
192, LINK]
offers the prospect of powerful new tools for the treatment of human
diseases and the improvement of human biological systems. Previous
papers have explored theoretical designs for artificial mechanical
red cells (respirocytes
[2,
LINK]) and artificial mechanical platelets (clottocytes
[3,
LINK]). This
paper presents a scaling study for artificial mechanical phagocytes
of microscopic size, called "microbivores."
Microbivores constitute a large class of medical nanorobots intended
to be deployed in human patients for a wide variety of antimicrobial
therapeutic purposes, as, for example, a first-line response to
septicemia. The analysis here focuses on a relatively simple device:
an intravenous (I.V.) microbivore whose primary function is to
destroy microbiological pathogens found in the human bloodstream,
using the "digest and discharge" protocol first described by the
author elsewhere [1,
LINK,LINK].
A separate analysis would be required to design devices intended to
clear bacterial infections from nonsanguinous spaces such as the
tissues, though such devices would undoubtedly have much in common
with the microbivores described herein.

After a basic overview of current approaches to
sepsis and septicemia that defines the medical challenge, the basic
microbivore scaling design is presented, followed by a brief
analysis of the phagocytic activity and pharmacokinetics of
bloodborne nanorobotic microbivores. As a scaling study, this paper
serves mainly to demonstrate that all systems required for
mechanical phagocytosis could fit into the stated volumes and could
apply the necessary forces and perform all essential functions
within the given power limits and time allotments. This scaling
study is neither a complete design nor a formal design proposal.

2. Sepsis and Septicemia

Sepsis [4]
is a pathological state, usually febrile, resulting from the
presence of microorganisms or their poisonous products in the
bloodstream [5].
Microbial infection may manifest as cellulitis (local dissemination
of infection), lymphangitis or lymphadenitis (dispersion along
lymphatic channels) or septicemia (widespread dissemination via the
bloodstream). Septicemia, also known as blood poisoning, is the
presence of pathogenic microorganisms in the blood. If allowed to
progress, these microorganisms may multiply and cause an
overwhelming infection. Symptoms include chills and fever, petechiae
(small purplish skin spots), purpuric pustules and abscesses. Acute
septicemia, which includes tachycardia, tachypnea, and altered
mental function, may combine with hypotension and inadequate organ
perfusion as septic shock -- the resulting decreased myocardial
contractility and circulatory failure can lead to widespread tissue
injury and eventually multiple organ failure and death [5],
often in as few as 1-3 days. Risk is especially high for
immune-compromised individuals -- in one animal study, the LD50*
for mice rendered leukopenic (defined as <10% normal leukocrit) was
less than 20 bacteria of the species Pseudomonas aeruginosa [6].
Asplenic patients are particularly susceptible to rapidly
progressive sepsis from encapsulated microorganisms such as
streptococcal pneumonia, hemophilus influenza and meningococcus, and
will die if the infection is not recognized rapidly and treated
aggressively.

* LD50
refers to the mean lethal dose which will kill 50% of the animals
receiving that dose.

2.1 Bacteremia

The healthy human bloodstream is generally considered
a sterile environment. Although bacterial nutrients are plentiful in
blood, major antimicrobial defenses include the circulating
neutrophils and monocytes capable of phagocytosis and the supporting
components of humoral immunity including complement and
immunoglobulins.

Still, it is not unusual to find a few bacteria in
blood. Normal activities like chewing, brushing or flossing teeth
causes movement of teeth in their sockets, infusing a burst of
commensal oral microbes into the bloodstream [7].
Bacteria can enter the blood via an injury to the skin, the lining
of the mouth or gums, or from gingivitis or other minor infections
in the skin and elsewhere [8].
Bacteremias from a focus of infection are usually intermittent,
while those from vascular system infection tend to be continuous [7],
such as endocarditis or embolism from heart valve vegetations in
subacute bacterial endocarditis (SBE), sometimes leading to
infectious mycotic (e.g., Staphylococcus aureus) aneurysms.

Bacteria can also enter the blood during surgical,
dental, or other medical procedures [8]
such as the insertion of I.V. lines (providing fluids, nutrition or
medications), cystoscopy (a viewing tube inserted to examine the
bladder), colonoscopy (a viewing tube inserted to view the colon),
or heart valve replacement with a prosthetic (thankfully now rare,
due to heavy preoperative dosing with cefazolin). Such bacteria are
normally removed by circulating leukocytes (along with the fixed
reticuloendothelial cells in the spleen, liver, and lungs), but a
few species of bacteria are unusually virulent and can overwhelm the
natural defenses. The CDC estimates that ~25,000 U.S. patients die
each year from bacterial sepsis [9].
Worldwide, there are ~1.5 million cases of sepsis and ~0.5 million
deaths from sepsis annually. Antibiotics can fight sepsis, pressors
can relieve hypotension from sepsis, volume replacement and I.V.
albumin or HESPAN (hetastarch) can offset hypovolemia, but until
recently there have been no pharmacological agents approved to fight
the complications of coagulation and inflammation due to bacterial
endotoxin (Section
4.4.2) (which can still lead to a mortality rate of 30%-50% [10])
although antiendotoxin peptides [242]
and anti-LPS monoclonal antibodies [243]
are being investigated for this purpose.

The recommended duration of therapy even for
uncomplicated cases of S. aureus bacteremia arising from a
removable source is 2-9 grams/day of antibiotics given I.V. for 2
weeks [11],
after which 5% of patients still relapse, usually with endocarditis.
Endocarditis accompanying bacteremic pneumonia in years past might
require a treatment regimen of penicillin G potassium in the
quantity of 24 million units/day, representing 15 grams/day
dissolved in a minimum I.V. infusate volume of 24 ml/day, for 4
weeks [11,
12];
the current most aggressive treatment is 0.5-2 gm/day vancomycin
orally for 7-10 days [12],
often together with 1-4 gm/day ceftriaxone and possibly also a
similar dose of teichoplanin (antibiotics of last resort, due to
potential toxicity).

2.1.3 Phage Therapy

An interesting emerging alternative to antibiotic
therapy -- and a small step towards nanomedicine -- is phage therapy
[14-27].
Bacteriophage viruses are tiny biological nanomachines that were
first employed against bacteria by d'Herelle in 1922 [14]
but were abandoned therapeutically (and then superceded by
antibiotics) after disappointments in early trials [22].
Bacteriophages may be viewed as self-replicating pharmaceutical
agents [26]
that can consume and destroy pathogenic bacteria when injected into
infected hosts. A single E. coli cell injected with a single
T4 phage at 37°C in rich media lyses after 25-30 minutes, releasing
100-200 phage particles; if additional T4 particles are added >4
minutes after the first, lysis inhibition is the result and the
bacterium will produce virions for up to 6 hours before it finally
lyses [15].
Of course, medical nanorobots will not be self-replicating [1].

With the relatively recent realization that phages
have a very narrow host range [27],
success rates of 80-95% have been reported [23]
and interest in phage therapy as an alternative to antibiotics is
reawakening [25].
For example, 106E. coli bacteria injected
intramuscularly into mice killed all of the animals (100%
mortality), but the simultaneous injection of 104 phage
virions specifically selected against the K1 capsule antigen of that
bacterial strain of E. coli completely prevented death (0%
mortality) [17].
Soothill [19]
found that a dose of 1.2 ×107 virions of a bacteriophage
targeted against a virulent strain of Pseudomonas aeruginosa
protected half of the mice who were challenged with 5 LD50 of the
bacterium; as few as 100 virions of another phage specifically
targeted against a virulent strain of Acinetobacter baumanii
protected mice challenged with 5 LD50 (108 CFU)*
of the pathogen. Interestingly, an oncolytic virus has recently been
reported [31].

One practical difficulty with phage therapy is
that even in the absence of an immune response, intravenous
therapeutic phage particles are rapidly eliminated from circulation
by the reticuloendothelial system (RES), largely by sequestration in
the spleen [16].
But Merril et al [27]
found that splenic capture could be greatly eliminated by the serial
passage of phage through the circulations of mice to isolate mutants
that resist sequestration. This selection process results in the
modification of the nature of the phage surface proteins, via a
double-charge change from acidic to basic which is achieved by
replacing glutamic acid (- charge) with lysine (+ charge) at the
solvent-exposed surface of the phage virion [27].
The mutant virions display 13,000-fold to 16,000-fold greater
capacity to evade RES entrapment 24 hours post-injection as compared
to the original phage [27].
But one concern is that since evasion of entrapment allows increased
virulence for most pathogens, widespread use of such modified virus
could make possible species jumping of the altered phage genes,
especially if the virion is RNA-based and has a high mutation rate.
Nanorobotic agents entirely avoid this risk.

* The number
of bacterial cells present is often reported as colony-forming
units, or CFU.

2.1.4 Bacterial Shape, Size, and Intravenous LD50

Bacteria are unicellular microorganisms capable of
independent metabolism, growth, and replication. Their shapes are
generally spherical or ovoid (cocci), cylindrical or rodlike
(bacilli), and curved-rod, spiral or comma-like (spirilla). Bacilli
may remain associated after cell division and form colonies
configured like strings of sausages. Bacteria range in size from
0.2-2 microns in width or diameter, and from 1-10 microns in length
for the nonspherical species; the largest known bacterium is
Thiomargarita namibiensis, with spheroidal diameters from 100-750
microns [32].
Spherical bacteria as small as 50 nm in diameter have been reported
[33]
and disputed [34],
but it has been theorized [35]
that the smallest possible cell size into which the minimum
essential molecular machinery can be contained within a membrane is
a diameter of ~40-50 nm. Many spherical bacteria are ~1 micron in
diameter; an average rod or short spiral cell might be ~1 micron
wide and 3-5 microns long. However, most bacteria involved in
bacteremia and sepsis are <2 micron3 in volume (Table
1).

Table 1. Size and Shape of
Microbes Most Commonly Involved in Bacteremia [36]

Bacterial Species

Shape

Diameter (micron)

Length (micron)

Volume (micron3)

Francisella tularensis

rod

0.2

0.3-0.7

0.01-0.02

Klebsiella pneumoniae

ovoid

0.4

----

0.05

Campylobacter
spp.

rod

0.2-0.4

1.5-3.5

0.05-0.50

Vibrio cholerae

rod

0.3

1.3

0.10

Streptococcus pyogenes

ovoid

0.6-1.0

----

0.10-0.50

Pseudomonas aeruginosa

rod

0.3-0.5

1-3

0.10-0.60

Brucella
spp.

rod

0.5-0.7

0.5-1.5

0.10-0.60

Yersinia pestis

rod

0.4-0.8

0.8-3

0.10-1.50

Listeria monocytogenes

rod

0.5

1.3

0.25

Erysipelothrix rhusiop.

rod

0.5

1.3

0.25

Salmonella typhi

rod

0.4-0.6

2-3

0.25-0.85

Escherichia coli

rod

0.5-0.65

1.7-2.0

0.33-0.66

Staphylococcus
spp.

sphere

0.5-1.5

----

0.07-1.75

Neisseria
spp.

sphere

1

----

0.50

Moraxella catarrhalis

rod

1

2-3

1.60-2.35

Shigella
spp.

rod

1

2-3

1.60-2.35

The intravenous median lethal dose (LD50) for 50%
of hosts inoculated with various bacteremic microorganisms ranges
widely from 1-109 CFU/gm (Table
2), but the central range appears to be 0.1-100 ×106
CFU/ml assuming a ~1 gm/cm3 density for biological
materials.

2.2 Viremia

Viremia is the presence of virus particles in the
bloodstream, usually a transient condition [7].
Viruses are acellular bioactive parasites that attack virtually
every form of cellular life. Viruses have diameters ranging from
16-300 nm [52]
-- for example, poliomyelitis ~18 nm, yellow fever ~25 nm,
adenovirus (common cold) ~70 nm, influenza (flu) ~100 nm, herpes
simplex and rabies ~125 nm, and psittacosis ~275 nm [53].
Their shape is either pseudospherical with icosahedral symmetry, as
in the poliomyelitis virus, or rodlike, as in the tobacco mosaic
virus (TMV). A virus surrounded only by protein coat (capsid) is a
naked virus; some viruses (e.g., HIV, HSV, pox), called enveloped
viruses, acquire a lipid membrane envelope from their host cell upon
release.

In cases of blood plasma viremia, virion particle
counts range from 1/ml to 0.35 ×106/ml for HIV in humans
[54-56],
with a mean of 25/ml for asymptomatic patients; viral loads for
simian immunodeficiency virus (SIV) in monkeys may be much higher,
2-200 ×106/ml of blood [57].
Hepatitis C (HCV) [58]
infectious viral loads (at ~10-18 gm/virion)
are considered low at 0.2-1 × 106/ml, medium at 1-5 ×106/ml,
high at 5-25 ×106/ml, and very high at >25 ×106/ml.
Hepatitis G (HGV) [59]
viral loads in symptomatic patients are 0.16-5.1 ×106/ml.
TT virus (TTV) [60]
loads in HIV patients may exceed >0.35 ×106/ml. Thus the
typical blood particle burdens in viremia are much the same as in
bacteremia, roughly 0.1-100 ×106/ml. Viral infections can
be very difficult to eradicate pharmaceutically, as most treatments
are virustatic, not virucidal. For example, acute treatment of
herpesvirus requires 2 grams/day of acyclovir, with chronic
suppressive therapy for recurrent disease requiring 0.8 grams/day
for up to 12 months [12].

2.3 Fungemia

In severely immunocompromised patients, fungi may
gain access to the bloodstream, producing fungemia [7].
Fungal cells in peripheral blood are typically ovoid to elongated,
from 3 × 3 microns up to 7 ×10 microns in size, and occur singly,
budding, or in short chains and clusters [61].
Candidal fungemia is most common; Candida albicans blood
counts in human patients are considered "ultralow" at < 1 CFU/ml and
"low" at 1-3 CFU/ml in neonates [62],
but "high" at > 5 CFU/ml in adult patients [63];
in one test series, fungemic patients showed 5.5 CFU/ml in venous
blood and 9.1 CFU/ml in arterial blood, suggesting that peripheral
tissues may clear ~40% of yeasts [64].
Rats injected with ~100 ×106 CFU/ml of C. albicans
all died in < ~6 hours from nonendotoxemic (i.e., non-LPS related)
shock [65].

2.4 Parasitemia and Rickettsemia

Parasitemia arises from parasites that have evolved
to live in the bloodstream include the Plasmodium (malaria)
family and the flagellate protozoans Trypanosoma (sleeping
sickness) and Leishmania (leishmaniasis). Blood parasites
typically have a juvenile form that is ovoid or ring-shaped with
dimensions of 1-5 microns, and an adult tubular form measuring 1-5
microns in width and 10-30 microns in length [68].
In Trypanosoma brucei, the number of trypanosomes in blood
fluctuates in waves, and the organisms are typically undetectable
for 3 out of 5 days [69].
Trypomastigotes have an I.V. LD50 in mice of ~2.5/gm [70,
71]. Trypanosoma brucei gambiense inoculated into mice
has an LD50 of 0.02-0.15 ×106 trypanosomes/gm, with
growth rates slowing at organism blood concentrations > 300 ×106
trypanosomes/ml and death occurring at a blood parasite load of 2000
×106 trypanosomes/ml [72].
Malaria may be treated with several oral doses of chloroquine
phosphate totalling 2.5 gm over three days, but there is increasing
microbial resistance to chloroquine worldwide and as little as 1 gm
of the medicine can be fatal in children, with toxic symptoms
appearing within minutes of overdosage [12];
a single 1.25 gm dose of mefloquine is sometimes effective in mild
cases [12].

Rickettsia are
rod-shaped or coccoid gram-negative obligate intracellular parasites
~0.25 microns in diameter that in humans grow principally in
endothelial cells of small blood vessels, producing vasculitis, cell
necrosis, vessel thrombosis, skin rashes and organ dysfunctions [73].
The infection is characterized by repetitive cycles of bloodborne
organisms, or rickettsemia. For example, in cattle the number of
pathogens in the blood varies between a low of 100/ml and a peak of
1-10 ×106/ml over 6-8 week intervals; in each cycle, the
blood count slowly rises over 10-14 days and then declines
precipitously [74].
However, most of these parasites are found in the red cells, and the
organism's appearance in the blood plasma is incidental to its
activity. Plasma titers for free R. rickettsii organisms in
the blood of human patients with Rocky Mountain spotted fever
averaged 5-16 parasites/ml in treated patients who survived, and
1000 parasites/ml in the postmortem plasma of one patient with
untreated fatal fulminant fever [75].
Antibiotic therapy has reduced the death rate from 20% to about 7%,
with death usually occurring when treatment is delayed [8].

3. Microbivore Scaling Analysis and Baseline
Design

The foregoing review suggests that existing
treatments for many septicemic agents often require large quantities
of medications that must be applied over long periods of time, and
often achieve only incomplete eradication, or merely growth arrest,
of the pathogen. A nanorobotic device that could safely provide
quick and complete eradication of bloodborne pathogens using
relatively low doses of devices would be a welcome addition to the
physician's therapeutic armamentarium. The following analysis
assumes a bacterial target (e.g. bacteremia), although other targets
are readily substituted (Section
4.4).

The microbivore is an oblate spheroidal
nanomedical device consisting of 610 billion precisely arranged
structural atoms plus another 150 billion mostly gas or water
molecules when fully loaded (Section
3.2.5). The nanorobot measures 3.4 microns in diameter along its
major axis and 2.0 microns in diameter along its minor axis, thus
ensuring ready passage through even the narrowest of human
capillaries (~4 microns in diameter [1,
LINK]).
Its gross geometric volume of 12.1056 micron3 includes
two normally empty internal materials processing chambers totalling
4 micron3 in displaced volume. The device may consume up
to 200 pW of continuous power while in operation and can completely
digest trapped microbes at a maximum throughput of 2 micron3
per 30-second cycle, large enough to internalize almost all relevant
microbes in a single gulp. As in previous designs [2],
to help ensure high reliability the system presented here has
tenfold redundancy in all major components, excluding only the
largest passive structural elements.

During each cycle of operation, the target
bacterium is bound to the surface of the microbivore via
species-specific reversible binding sites [1,
LINK].
Telescoping robotic grapples emerge from silos in the device
surface, establish secure anchorage to the microbe's plasma
membrane, then transport the pathogen to the ingestion port at the
front of the device where the cell is internalized into a
morcellation chamber. After sufficient mechanical mincing, the
morcellated remains are pistoned into a digestion chamber where a
preprogrammed sequence of engineered enzymes are successively
injected and extracted, reducing the morcellate primarily to
monoresidue amino acids, mononucleotides, glycerol, free fatty acids
and simple sugars, which are then harmlessly discharged into the
environment through an exhaust port at the rear of the device,
completing the cycle.

This "digest and discharge" protocol [1,
LINK,LINK]
is conceptually similar to the internalization and digestion process
practiced by natural phagocytes, but the artificial process should
be much faster and cleaner. For example, it is well-known that
macrophages release biologically active compounds such as muramyl
peptides during bacteriophagy [76],
whereas well-designed microbivores need only release biologically
inactive effluent.

3.1 Primary Phagocytic Systems

The principal activity which drives microbivore
scaling and design is the process of digestion of organic
substances, which also has some similarity to the digestion of food.
The microbivore digestive system has four fundamental components --
an array of reversible binding sites to initially bind and trap
target microbes (Section
3.1.1), an array of telescoping grapples to manipulate the
microbe, once trapped (Section
3.1.2), a morcellation chamber in which the microbe is minced
into small, easily digested pieces (Section
3.1.3), and a digestion chamber where the small pieces are
chemically digested (Section
3.1.4).

3.1.1 Reversible Microbial Binding Sites

The first function the microbivore must perform is to
acquire a pathogen to be digested. A collision between a bacterium
of the target species and the nanorobotic device brings their
surfaces into intimate contact, allowing reversible binding sites on
the microbivore hull to recognize and weakly bind to the bacterium.
Binding sites can already be engineered [77,
78].
Bacterial membranes are quite distinctive, including such obvious
markers as the family of outer-membrane trimeric channel proteins
called porins in gram-negative bacteria like E. coli [79,
80] and other surface proteins such as Staphylococcal protein A
[81]
or endotoxin (lipopolysaccharide or LPS), a variable-size
carbohydrate chain that is the major antigen of the outer membrane
of gram-negative bacteria. Mycobacteria contain mycolic acid in
their cell walls [82].
And only bacteria employ right-handed amino acids in their cellular
coats, which helps them resist attack by digestive enzymes in the
stomach and by other organisms. Peptidoglycans, the main structural
component of bacterial walls, are cross-linked with peptide bridges
that contain several unusual nonprotein amino acids and D-enantiomeric
forms of Ala, Glu, and Asp [83].
D-alanine is the most abundant D-amino acid found in most
peptidoglycans and the only one that is universally incorporated [84].
Macrophages have evolved a variety of plasma membrane receptors that
recognize conserved motifs having essential biological roles for
pathogens, hence the surface motifs are not subject to high mutation
rates; these pathogen receptors on macrophages have been called
"pattern recognition receptors" and their targets
"pathogen-associated molecular paterns" [246].
Genomic differences between virulent and non-pathogenic bacterial
strains [85]
likely produce phenotypic differences that could enable the biasing
of nanorobots towards the detection of the more toxic variants, if
necessary.

Additionally, all bacteria of a given species
express numerous unique proteins in their outermost coat. A complete
review is beyond the scope of this paper, but a few representative
examples can be cited. Each single-celled Staphylococcus aureus
organism displays binding sites for human vitronectin on its
surface, including 260 copies/cell representing high-affinity sites
and 5,240 copies/cell representing moderate-affinity sites [86].
The plasmid-specified major outer membrane protein TraTp of
Escherichia coli is normally present in 21,000 copies/cell at
the cell surface [87].
Streptococcus pyogenes (strain 6414) has 11,600 copies/cell
of surface binding sites to human collagen [88];
another receptor protein specific to type II collagen (among the
dozens of collagen types) are found in 30,000 copies/cell on the
surface of each Staphylococcus aureus (strain Cowan 1) cell
with equilibrium constant Kd
= 10-7 M [89].
(Researchers found that the same bacterial receptor would also
specifically respond to synthetic collagenlike analogs containing
the peptide sequences (Pro-Gly-Pro)n, (Pro-Pro-Gly)10,
and (Pro-OH-Pro-Gly)10 [89].)
If the microbivore must distinguish among ~500 different bacterial
species or strains, then each bacterial cell type may be uniquely
identified using as few as log2(500) ~ 9 binary antigenic
markers [1,
LINK].

Assuming that nine species-specific bacterial coat
ligands are sufficient to uniquely identify an encountered bacterium
as belonging to the target species or strain, and that ~104
copies of each of the nine ligands are present on a bacterial
surface of area ~10 micron2, then the mean distance
between each ligand of the same type is 31.6 nm. A square array of
200 adjacent ligand receptors on the nanorobot surface, with each
ligand or receptor active site ~5 nm2 in area (e.g.,
antibody-antigen complexes typically show contact interfaces of 6-9
nm2, involving 14-21 residues on each side [90-92]),
would on average overlap one such ligand that is resident in a
bacterial surface pressed against it. If there are 100 such arrays
uniformly distributed over the entire nanorobot surface, then a
randomly chosen mutual contact area of only 1% of the nanorobot
surface suffices to ensure that there is at least one array
overlapping a unique ligand on the bacterial surface during a
collision. Of course, the probability of binding, even given mutual
contact, is not unity, but perhaps only ~10% (e.g.,
Nencounter ~ 10 [1,
LINK]).
However, this factor is almost completely offset because there are
nine equivalent array sets -- one set for each of the nine unique
bacterial ligands -- and recognition and binding of any one of the
nine unique ligands will suffice to bind the bacterium securely to
the nanorobot.

Since array members need not be adjacent, the
actual physical configuration on the microbivore surface is a bit
different. The binding sites are modeled after the narrowband
chemical sensor described in Nanomedicine [1,
LINK],
Figure 4.2.
Each 3×3 receptor block consists of nine 7 nm × 7 nm receptor sites,
one for each of the nine species-specific bacterial coat ligands.
There are 20,000 of these 3×3 receptor blocks distributed uniformly
across the microbivore surface. Each 3×3 receptor block measures 21
nm × 21 nm ×10 nm. A single receptor, if bound to a ligand, may
provide a binding force of 40-160 pN [1,
LINK],
probably larger than the largest plausible in sanguo dislodgement
force of ~100 pN [1,
LINK]
and thus gripping the bacterium reasonably securely. The recognition
event can be consumated in tmeas
~ 30 microsec, according to Eqn. 8.5 from Nanomedicine [1,
LINK].
As an operational procedure, once any one of the nine key ligands
has been detected, all of the remaining unoccupied receptors for
that ligand in other receptor blocks can be deactivated, and so on
until all nine ligands have been individually confirmed -- a
combination lock whose completion triggers bacteriocide.
Interestingly, during phagocytosis by macrophages most injected
particles are recognized by more than one receptor; these receptors
are capable of cross-talk and synergy, and phagocytic receptors can
both activate and inhibit each other's function [247].

Microbial binding is energetically favored; if
binding energy is ~240 zJ per microbial ligand [1,
LINK] (1
zeptojoule (zJ) = 10-21 J), then the power
requirement for debinding a set of 9 occupied receptors in ~100
microsec is only ~0.02 pW.

3.1.2 Telescoping Grapples

Once the target bacterium has been confirmed and
temporarily secured to the microbivore surface at >9 points with a
minimum binding force of >360-1440 pN, telescoping robotic grapples
emerge from silos in the nanodevice surface to establish secure
anchorage to the microbe's plasma membrane or outer coat. Each
grapple is mechanically equivalent to the telescoping robotic
manipulator arm described by Drexler [93],
but 2.5 times the length. This manipulator when fully extended is a
cylinder 30 nm in diameter and 250 nm in length with a 150-nm
diameter work envelope (to the microbivore hull surface), capable of
motion up to 1 cm/sec at the tip at a mechanical power cost of ~0.6
pW at moderate load (or ~0.006 pW at 1 mm/sec tip speed), and
capable of applying ~1000 pN forces with an elastic deflection of
only ~0.1 nm at the tip. (Interestingly, supplementing
chemispecificity (Section
3.1.1) gram-negative bacteria can be distinguished from
gram-positive organisms by their wavy surface appearance when
scanned by AFM [94],
a subtle morphological difference that should also be detectable by
grapple-based pressure sensors that could help confirm microbial
identity.)

Each telescoping grapple is housed beneath a
self-cleaning irising cover mechanism that hides a vertical silo
measuring 50 nm in diameter and 300 nm in depth, sufficient to
accommodate elevator mechanisms needed to raise the grapple to full
extension or to lower it into its fully stowed position. At a 1
mm/sec elevator velocity, the transition requires 0.25 millisec at a
Stokes drag power cost (operating in human blood plasma) of 0.0008
pW, or 0.008 pW for 10 grapples maximally extended simultaneously [1,
LINK].
The elevator mechanism consists of compressed nitrogen gas rotored
into or out of the subgrapple chamber volume from a small
high-pressure sealed reservoir, a pneumatic piston providing the
requisite extension or retraction force. A grapple-distension force
of ~100 pN applied for a distance of 250 nm could be provided by 25
atm gas pressure in a minimum subgrapple chamber volume of 104
nm3, involving the importation of ~6000 gas molecules.
Removal of these ~6000 gas molecules from a maximum subgrapple
chamber volume of 105 nm3 provides a ~1 atm
pressure differential and a maximum grapple-retraction force of ~100
pN; cables or other mechanisms may assist in retraction if more
force is needed. The aperture of the irising silo cover can be
controlled to continuously match the width of the protruding
grapple, greatly reducing the intrusion of foreign biomolecules into
the silo.

Each grapple is terminated with a reversible
footpad ~20 nm in diameter. In the case of gram-positive bacteria, a
footpad may consist of 100 close-packed lipophilic binding sites
targeted to plasma membrane surface lipid molecules, providing a
secure 1000 pN anchorage between the nanorobot and the bacterium
assuming a single-lipid extraction force of ~10 pN [1,
LINK].
In the case of gram-negative bacteria, a footpad with binding sites
for ~3 murein-linked covalently attached transmembrane protein
molecules would provide a secure 120-480 pN anchorage, assuming
40-160 pN/molecule and ~9 such molecules per 1000 nm2 of
microbial surface (Section
3.1.1). In either case, undesired adhesions with bacterial slime
must be avoided. The footpad tool is rotated into, or out of, an
exposed position from behind a protective cowling, using
countercoiled internal pull cables.

The tiniest bacterium to be digested may be ~200
nm in diameter (Section
2.1.4), but the smallest virus can be only ~16 nm wide (Section
2.2). Since the work envelopes of adjacent grapples picking
particles bound to the hull surface extend 150 nm toward each other
from either side, the maximum center-to-center intergrapple
separation that permits the ciliary transport of 16 nm objects is
~300 nm. This requires 1 grapple per 0.09 micron2 of
nanorobot surface, for a total of 277 grapple silos uniformly
distributed over the entire 26.885 micron2 microbivore
outer hull, excluding the two 1-micron2 port doors. (One
or more grapple-containing bridges across the annular exhaust port
aperture (Section
3.1.4) may be necessary if it is desired to transport targets
<200 nm in diameter from the circular DC exhaust port island to the
main grapple field of the microbivore, allowing subsequent transport
to the ingestion port inlet; such bridges are not included in the
present design.) During transport, a bacterium of more typical size
such as a 0.4 micron × 2 micron P. aeruginosa bacillus may be
supported by up to 9 grapples simultaneously. A somewhat larger
E. coli bacterium would be supported by up to 12 grapples.

After telescoping grapples are securely anchored
to the captive bacterium, the receptor blocks are debonded from the
microbial surface, leaving the grapples free to maneuver the
pathogen as required. Grapple force sensors inform the onboard
computer of the captive microbe's footprint size and orientation.
The grapples then execute a ciliary transport protocol in which
adjacent manipulators move forward and backward countercyclically,
alternately binding and releasing the bacterium, with new grapples
along the path ahead emerging from their silos as necessary and
unused grapples in the path behind being stowed. Manipulator arrays,
ciliary arrays (MEMS), and Intelligent Motion Surfaces are related
precursor (and currently available) technologies (reviewed in
Section 9.3.4
of Nanomedicine [1,
LINK]).

Rodlike organisms are first repositioned to align
their major axis perpendicular to a great circle plane containing
both the device center point and the ingestion port at the front of
the device. This keeps the organism traveling over surfaces having
the largest possible radius of curvature during transport, thus
minimizing any forces necessary to bend the bacterium as it follows
the curved microbivore surface. A cylindrical bacterium of length
Ltube and bending stiffness
ktube is bent by a force F into a circle segment having
radius of curvature Rcurve ~
(ktubeLtube2
/ 2 F) for small deflections.
For the bacillus P. aeruginosa, Ltube
~ 2 microns and tube radius is ~0.2 microns; the elastic modulus is
2.5 ×107 N/m2 for the 3-nm thick hydrated
sacculus [97],
giving ktube~ 4 ×10-4
N/m using Eqn. 9.50 from
Nanomedicine [1,
LINK].
To bend the microbe to the semimajor axis of the microbivore (Rcurve
= 1.7 microns) requires F ~ 470
pN, or F ~ 800 pN for the
semiminor axis (Rcurve = 1
micron), both of which are substantial bending forces in comparison
to the nominal single-grapple anchorage force of 100-500 pN/footpad.
Thus it is desirable to bend the bacterium as little as possible
during transport. Bending forces may be minimized by adjusting
grapple lengths to hold the bacillus farther from the microbivore
surface near the endpoints of the footprint, and closer to the
microbivore surface near the center of the footprint.

Organisms of all shapes are conveyed toward the
ingestion port via cyclical ciliary cycling motions. At a transport
velocity of 1 mm/sec, a microbe captured at the greatest possible
distance from the ingestion port (~3 microns) is moved to the
vicinity of the ingestion port in ~3 millisec. The Stokes law energy
cost of transporting an E. coli bacterium through blood
plasma side-on at 1 mm/sec is 0.01 pW, so transport power is
dominated by mechanical losses in the grapples, a total of ~0.06 pW
if 10 grapples are operated simultaneously.

Because the ingestion port is slightly recessed
into the body of the nanorobot ellipsoid at the equator, the
approaching bacterium must be carried around an inlet rim having a
considerably smaller radius of curvature than the main body of the
microbivore. The inlet rim is essential in this design and provides
needed mechanical control from inlet-wall grapples as the microbe is
fed into the ingestion port. From simple geometry, if one grapple is
fully extended to length L =
Lgrap and the adjacent
grapple is almost fully retracted to length L ~ 0, then the bacillus can be
conveyed around an inlet rim curve of radius Rrim
with zero bending if the distance between the adjacent grapples is
no more than dmax ~ 2
Rrimsin-1
(Lgrap / 2
Rrim)½ ~ 0.39
microns, taking Lgrap = 250
nm and Rrim ~ 0.25 microns
at the inlet rim. This requires at least 1 grapple per
dmax2 ~ 0.15
micron2 of nanorobot surface near the ingestion port,
comfortably lower in number density than the 0.09 micron2/grapple
elsewhere on the hull. Nevertheless, to ensure full control of the
transported object near the ingestion port an additional 23 grapple
silos are non-uniformly distributed over the 10% of microbivore
surface nearest the ingestion port, sufficient to raise the mean
number density to 0.05 micron2/grapple in that region.
Thus there are a total of 300 grapple silos embedded in the entire
microbivore outer hull, excluding the area covered by the two
1-micron2 port doors.

3.1.3 Ingestion Port and Morcellation Chamber

The ingestion port door is an oval-shaped irising
mechanism [1,
LINK]
with an elliptical aperture measuring 0.8654 microns × 1.4712
microns, providing a 1 micron2 aperture when fully open.
Assuming 0.5 micron2 of contact surfaces sliding ~1
micron at 1 cm/sec, power dissipation is ~3 pW during the 0.1
millisec door opening or closing time. To allow handing small
particles like viruses securely into the ingestion port, the
porthole mechanism can be programmed to iris open in an off-center
manner if required. For example, if manipulating a small virion
particle the hole's center should initiate within 150 nm of a
sidemost edge of the port (i.e., within one grapple surface-reach
distance, either left or right side); after the growing aperture
reaches the edge of the nearest side, it can then continue to dilate
toward the edge on the opposite side while retaining its expanding
elliptical shape. On the other hand, if a bacterium >~0.632 microns
in diameter is being manipulated, the port door may be programmed to
iris open from the center. During internalization the port doors
perform gentle test-closings, with associated force sensors
providing feedback as to the completeness of the internalization
process and enabling the microbivore to detect the pinch points of
linked bacilli to allow separation at these points, if necessary. In
the case of motile bacilli having long flagellar tails, the
premature closing of the ingestion port door may sever the tail,
casting the immunogenic tail fragment adrift in the blood; this
outcome must be avoided (Section
4.3).

Opening the ingestion port door allows entry into
the morcellation chamber (MC), a cylindrical chamber 2 microns in
length and the same interior elliptical cross-section as the port
door, giving a total open volume of 2 micron3 which is
large enough to hold one intact microorganism because most
sepsis-related bacteria are <2 micron3 in volume (Table
1). Recessed into the MC walls are 10 diamondoid cutting blades
(possibly multisegmented), each ~2 micron long, ~0.25 micron wide,
and 10 nm thick with a 1 nm cutting edge, giving ~0.050 micron3
of blades (~0.005 micron3/blade). Following the analysis
of nano-morcellation systems described elsewhere [1,
LINK], to
mince material having Young's modulus ~108 N/m2
using one blade at a time (reserving the other 9 blades as
replacements or to provide alternative chopping geometries) requires
the application of ~100 nN/chop, consuming up to ~100 pW during a
process in which the blade reciprocates at 50 Hz and travels at ~60
micron/sec, making 20 cuts in a total mincing time of 400 millisec.
(Bacterial walls include a 3-6 nm thick hydrated sacculus [97]
and include a cross-linked peptidoglycan (murein) mesh [95-97]
with strands spaced ~1.3 nm apart [98].)
The resulting morcellate should consist largely of organic chunks
~3-10 nm in diameter [1,
LINK].
An intriguing alternative configuration is a diamondoid sieve or
dragnet that could be pulled repeatedly through the MC, analogous to
pushing the microbe forcibly through a strainer; other possible
fragmentation techniques such as sonication appear to require too
much onboard acoustic energy to be feasible (e.g., power intensities
of ~106 pW/micron2 [1,
LINK]).

Once microbial mincing is complete, the morcellate
must be removed to the digestion chamber (Section
3.1.4) using an ejection piston. A 20-nm thick piston pusher
plate driven by a 2 micron long, 10 nm thick pusher cable (energized
by the chopping blade motor coupled through a mechanical
transmission gearbox) comprises ~0.02 micron3 of device
volume. This piston moves forward at ~20 microns/sec, applying ~1
atm of pressure to push morcellate of viscosity ~100 kg/m-sec
through a 1 micron2 gated annular aperture for a chamber
length of 2 microns, emptying the MC in ~100 millisec with a
Poiseuille fluid flow power dissipation [1,
LINK] of
~2 pW. Interestingly, the energy dissipation rate required to
disrupt the plasma membrane of ~95% of all animal cells transported
in forced turbulent capillary flows is on the order of 108-109
W/m3 [101],
corresponding to a mechanical power input of 100-1000 pW into a 1
micron3 chamber volume. The annular MC/DC interchamber
door must be opened before activating the MC ejection piston; its
size and power specifications are similar to those of the annular DC
exhaust port door (Section
3.1.4.4).

The MC ejection piston also is used initially to
draw the microbe into the MC in a controlled manner. By slowly
pulling a vacuum after the ingestion port door has opened, the
piston can apply ~1 atm of negative pressure over the ~1 micron2
leading surface of the bacterium, or up to ~100 nN of force. The
Poiseuille flow of a microorganism of viscosity ~1000 kg/m-sec
through a 1 micron2 aperture with a 1 atm pressure
differential into a chamber 2 microns in length dissipates 0.2 pW as
the bacterium is drawn into the chamber at a speed of 2 microns/sec,
thus requiring ~1 second for complete internalization of 2 micron3
of ingesta.

3.1.4 Digestion Chamber and Exhaust Port

The digestion chamber (DC), like the MC, has a total
open volume of 2 micron3. The DC is a cylinder of oval
cross-section surrounding the MC, measuring roughly 2.0 microns in
width, 1.3 microns in height, and 2.0 microns in length, with a mean
~0.5 micron clearance between the DC and MC walls and a materials
volume of 0.11 micron3 assuming diamondoid walls ~10 nm
thick. Morcellate is pumped from the MC into the DC where a
preprogrammed sequence of engineered enzymes are successively
injected and extracted, reducing the morcellate primarily to
monoresidue amino acids, mononucleotides, free fatty acids and
monosaccharides, which are then harmlessly discharged into the
environment.

If the morcellate consists of organic chunks ~3-10
nm in diameter (Section
3.1.3), enzymes directed against specific bond types may attack
these bonds only if they are exposed on the outermost surface of
each chunk. Considering for simplicity only proteinaceous chunks,
and given that the average amino acid has a molecular weight of
141.1 daltons and a molecular volume of Vres
~ 0.49 nm3, then a chunk of volume
Vchunk may be regarded as having
Nlayer successive surface
layers where Vchunk ~
Vres (1 + 2Nlayer)3.
Taking Vchunk1/3
= 10.2 nm for the largest pieces implies a chunk comprised of 2197
residues and having Nlayer ~
6 layers that must be processed sequentially, like peeling an onion
one skin at a time. Thus the entire enzyme suite must be shuttled in
and out of the DC six times, with one "layer" of all chunks being
processed during each of the six subcycles.

3.1.4.1 Artificial Enzyme Suite

Artificial digestive enzymes may be designed to
attack just one class of chemical bond [102].
For example, the natural serine protease enzyme chymotrypsin only
cleaves peptide bonds at the carboxylic ends of residues having
large hydrophobic side chains, such as the aromatic amino acids
phenylalanine, tryptophan, and tyrosine [103,
104]. The proteolytic enzyme trypsin exhibits a different
specificity, cleaving peptide bonds on the C-terminal side of the
basic residues arginine and lysine [103].
The endopeptidase elastase attacks bonds adjacent to small amino
acid residues such as alanine, glycine, and serine [105]
and will cleave tri-, tetra-, and penta-peptides of alanine [104].
Enzymes which will cleave the unusual right-handed (D-enantiomeric)
amino acids found in bacterial coats, including D-aminopeptidase [106]
or D-stereospecific amino-acid amidase [107],
D-peptidase and DD-peptidase [107],
carboxypeptidase DD [108]
and D-amino acid acylase [109]
are well-known.

To prevent self-digestion during storage and use,
each artificial peptidase is engineered so that the class of residue
it is designed to attack is not exposed on its own external physical
surface [112]
-- that is, each artificial enzyme minimally exhibits strong
autolysis resistance [110-116],
with an ideal objective of near-zero autolysis. (A few natural
enzymes retain full post-autolysis functionality [117].)
Another significant design constraint is that natural bacterial
enzymes already present in the morcellate (e.g., elastase produced
by P. aeruginosa [118])
must have negligible activity against any of the microbivore's
artificial enzymes. Since the target microbe's enzyme inventory is
known in advance, the microbivore enzyme suite can be tailored to
deal with any unusually troublesome bacterial enzymes, and optimal
pH in the DC can be actively managed (see below).

Enzymes capable of degrading nucleic acid polymers
are classified as deoxyribonucleases (specificity for DNA) or
ribonucleases (specifically hydrolyzing RNA), or as exonucleases
(hydrolyzing a nucleotide only when present at a strand terminus,
moving in only one direction, either 3'®5'
or 5'®3') or endonucleases (cleaving
internal phosphodiester bonds to produce either 3'-hydroxyl and
5'-phosphoryl termini or 5'-hydroxyl and 3'-phosphoryl termini) [105].
Some endonucleases can hydrolyze both strands of a double-stranded
molecule, others attack only one strand of a double-stranded
molecule, while still others cleave only single-stranded molecules.
Restriction endonucleases recognize specific DNA sequences -- for
example, Hpa I recognizes a specific double-strand 6-base sequence
(GTTAAC/CAATTG) and selectively cleaves both strands of the double
strand in the middle at the TA/AT bond, producing an unreactive
molecular "blunt end" [105].
There are ten distinct dinucleotide bond combinations (AA, AC, AG,
AT, CC, CG, CT, GG, GT, and TT), which suggests that 10 artificial
endonucleases may suffice, plus 2 general-purpose dinucleases to
complete the digestion to mononucleotides, for a total of 12
artificial polynucleotidases.

Additional engineered enzymes (not included in the
present design) may be needed to digest bacteriophages that may be
resident inside certain bacteria. To avoid digestion by bacterial
restriction enzymes, phages often employ unusual molecular
substitutions involving 2,6-diaminopurine, 6-methyladenine,
8-azaguanine, 5-hydroxymethyl uracil, 5-methylcytosine,
5-hydroxymethylcytosine, and others [121].
For example, B. subtilis phage DNA replaces thymine with
hydroxymethyluracil and uracil; S-2L cyanophage replaces adenine by
2-aminoadenine (2,6-diaminopurine); SPO1, SP82G, and Phi-e
substitute hydroxymethyl dUTP for dTTP in the phage DNA up to 20%;
PBS1 and PBS2 phages substitute uracil for thymine; T-even
(T2/T4/T6) phage DNA replaces dCMP by hydroxymethylcytosine which is
then further glycosylated, rendering the phage DNA resistant to host
restriction; and in phage Mu DNA, a unique glycinamide moiety
modifies about 15% of the adenine residues [121].
Given our complete future knowledge of phage genomes and the
bacteria they are likely to inhabit, a comprehensive phage digestive
strategy can be planned and installed in advance, during microbivore
design and construction. This problem is not considered serious in
the case of standard antibiotic therapy.

Free adenosine (a mononucleotide) is involved in
the regulation of coronary blood flow [122],
and certain free nucleotides have been shown to exhibit minor
physiological action on lymphocytes [123]
and T cells [124]
in animal models, so additional nucleotidases, phosphatidases and
nucleosidases may be added if necessary to reduce free
mononucleotides to phosphoric acid, sugars, and purine/pyrimidine
bases prior to discharge from the nanorobot. However, such
additional enzymes are not included in the present microbivore
design because nucleotidase is naturally present in normal human
serum [125-129]
and at elevated serum levels in many disease conditions [129-133].

Microbial lipids may be digested by analogs of
pancreatic lipase (e.g., steapsin) or lipoprotein lipase which
hydrolyze polyacylglycerols (mostly glycosyl diacylglycerols in
bacteria) containing fatty acid chains into free fatty acids and
glycerol, by cholesterol esterase that hydrolyzes cholesteryl esters
into free cholesterol (although cholesterol and other sterols are
relatively rare in microorganisms [134-136]),
by phospholipase that attacks phospholipids producing glycerol,
fatty acids, phosphoric acid, and perhaps choline [105],
or by sphingolipidases [137]
or ceramidases [138]
that hydrolyze the sphingolipids found in some bacteria, resulting
in mostly glycerol and saturated (in bacteria) free fatty acids in
the final digesta. Acyloxyacyl hydrolase removes the secondary
(acyloxyacyl-linked) fatty acyl chains from the lipid A region of
bacterial lipopolysaccharides (LPS endotoxin), thereby detoxifying
the molecules [139].
The present microbivore design assumes a requirement for 5
artificial lipases.

Microbial carbohydrates may be digested by an
amylase that hydrolyzes starch and glycogen, and by a selection of
oligosaccharidases (e.g., maltase, sucrase-isomaltase) and
disaccharidases or saccharases (e.g., lactase, invertase, sucrase,
trehalase) to complete the digestion to monosaccharides [105].
(Lactase also has a second active site for splitting
glycosylceramides [105].)
The present design assumes a requirement for 4 artificial
carbohydrases in the microbivore enzyme suite.

Finally, simple anions or cations may be required
for pH management of the morcellate, and 25% of all enzymes contain
tightly bound metal ions or require them for activity [105],
most commonly Mg++, Mn++, Ca++, or
K+; certain low-bioavailability but essential cofactors
such as iron and copper might also need to be actively managed. It
might also be necessary in some cases to inject and extract small
quantities of superoxide dismutase, catalase and chelating agents
such as metallothionein, ferritin, or transferrin to control
potentially damaging concentrations of superoxides and metals in the
morcellate, or small quantities of other specialized enzymes
analogous to heme oxygenase, biliverdin reductase and
beta-glucuronidases to digest bacterial porphyrins [244],
enzymes [245]
to cleave bacterial rhodopsins, and so forth, but a full analysis of
these factors is beyond the scope of this paper. The present design
assumes a requirement for 3 additional chemical species of this
type, to be manipulated simultaneously with the artificial enzymes
as previously described.

Full digestion of the morcellate, constituting one
complete digestion cycle, is thus presumed to require six subcycles
of activity, with each subcycle involving the serial injection and
extraction of 40 different enzymes or enzyme-related molecules
(i.e., 40 sub-subcycles per subcycle), one after the other, for a
total of 240 enzyme sub-subcycles. Interestingly, intracellular
lysosomes are known to contain ~40 digestive enzymes capable of
degrading all major classes of biological macromolecules --
including at least 5 phosphatases, 4 proteases, 2 nucleases, 6
lipases, 12 glycosidases, and an arylsulfatase [140,
141].

3.1.4.2 Digestion Cycle Time

The duration of each enzyme sub-subcycle depends
primarily upon two factors: (1) the speed of enzymatic action (Section
3.1.4.2.1), which may differ somewhat for each enzyme and each
substrate, and (2) the speed at which enzymatic molecules can be
rotored into and out of the DC (Section
3.1.4.2.2).

3.1.4.2.1 Speed of Enzymatic Action

If enzyme molecules are plentiful and substrate
molecules are rare (typically 1%-100% of the enzymes), the most
appropriate measure of enzymatic speed is the enzymatic efficiency (kcat
/ Km) = 1.5-28 ×107
molecules of substrate converted to product per second, per molar
concentration of enzyme, for a wide variety of enzymes [142].
Here, the Michaelis constant Km
is the substrate concentration that produces the half-maximal
reaction rate, and kcat is
the reaction rate in product molecules generated per unit time per
enzyme molecule.

However, for most of the digestion cycle the DC
environment consists of a relatively small number of temporarily
resident enzyme molecules floating in a sea of plentiful substrate.
Zubay [142]
notes that in this situation, the speed of enzymatic action is
considerably slower and kcat,
also known as the enzyme turnover number, is the most relevant
measure of enzyme catalytic activity.
Table
3 shows that for peptidases, kcat
ranges from ~10-1sec-1
to ~105sec-1, while for other
enzymes the range is even wider, from ~10-1sec-1 to ~108sec-1.
In the present scaling study, the mean kcat
for all artificial engineered enzymes used in the microbivore enzyme
suite, measured against representative substrates, is taken as a
midrange value (for all enzymes) of ~104sec-1
at physiological temperatures (~37°C).

Table 3. Values of Enzyme
Turnover Number (kcat)
for Various Enzymes on Representative Substrates

Enzyme

kcat
(sec-1)

Reference

Peptidases:

Aminopeptidase PC

0.19

143

Granulocyte elastase

6

144

b-fibrinogenase

44

145

Arginine ester hydrolase

91

146

Chymotrypsin

100

142

Lugworm protease

110

147

Neutral endopeptidase

120

148

Carboxypeptidase A

141

149

Entamoeba endopeptidase

172

150

b-lactamase

210

151

Astacus protease

380

152

Carboxypeptidase 3

490

153

Dipeptidyl peptidase IV

814

120

Neutral proteinase

1,200

148

Aminopeptidase A

1,400

154

Penicillinase

2,000

142

Proline iminopeptidase

135,000

155

Other Enzymes:

Lysozyme

0.5

142

DNA polymerase I

15

142

a-amylase

140

156

A. ficuum acid phosphatase

260

157

Serratia wild-type nuclease

980

158

Lactate dehydrogenase

1,000

142

P. aeruginosa lipase

3,000

159

Staphylococcal nuclease

3,880

160

Acetylcholinesterase

12,500

161

Acetylcholinesterase

14,000

142

Carbonic anhydrase IV

170,000

162

Carbonic anhydrase

1,000,000

142

Catalase

40,000,000

142

To estimate the time required for each enzymatic sub-subcycle, for
simplicity the initial morcellate of volume Vmorc
~ 2 micron3 is assumed to consist mostly of water
containing a volume fraction fprot
~ 0.30 (30%) of now-minced protein. The specific volume of the
average amino acid residue is taken as Vres
~ 0.49 nm3/residue and the required number of enzymatic
sub-subcycles is taken as Nessc
~ 240. Then the average number of peptide bond scissions per sub-subcycle
is Nbondx = (Vmorcfprot) / (VresNessc)
~ 5 ×106 bonds/sub-subcycle, and the processing time per
sub-subcycle is tenz ~
Nbondx / (kcatnenz)
where nenz is the number of
enzyme molecules injected into the morcellate during each sub-subcycle.
Taking nenz = 104
enzyme molecules and kcat =
104sec-1, then
tenz ~ 50 millisec/sub-subcycle.

Note that the diffusion time required by an enzyme
molecule of radius 3.47 nm at 37°C in a plasma-like fluid of
viscosity ~10-3 kg/m-sec (for molecular
diffusion) to achieve an RMS displacement equivalent to the ~0.5
micron clearance between the DC and MC chamber walls is ~2 millisec
(<< tenz), according to Eqn.
3.1 from Nanomedicine
[1,
LINK], so
the enzyme action during each sub-subcycle is not seriously
diffusion-limited. (The diffusion constant for a ~72 kDa fusion
protein in unmorcellated intact E. coli cytoplasm is
~7.7 ×10-12 m2/sec [163],
giving a diffusion time across 0.5 microns of ~16 millisec,
according to Eqn. 9.80 from Nanomedicine [1,
LINK].)

3.1.4.2.2 Speed of Enzyme-Transport Rotors

If nenz
enzyme molecules must be transferred during each sub-subcycle in a
transport time ttransport
using nrotor molecular
sorting rotors with each rotor operating at a constant transport
rate of krotor
molecules/rotor-sec, then nrotor
= nenz / (ttransportkrotor).
Each artificial enzyme molecule is assumed to consist of ~350
residues with a molecular weight of ~50 kDa and a molecular volume
of ~175 nm3, giving a molecular diameter of ~6.9 nm if
assumed spherical. Taking the excluded volume per enzyme molecule
binding site as 7 nm in diameter, a sorting rotor 8 nm thick with 10
receptors plus one 8-nm blank space per rotor requires an
enzyme-transport rotor circumference of 78 nm, giving a rotor
diameter of 25 nm and a rectangular face area and volume per rotor
of ~200 nm2 and ~5000 nm3, respectively [1,
LINK;
93].

What is the value of krotor
during enzyme extraction? The injection of 104 enzyme
molecules into the 2 micron3 digestion chamber produces
an enzyme concentration of ~10-5 M (~5
×10-6 molecules/nm3), giving an initial
rotor rate kr(1) ~ 10,000
molecules/rotor-sec for the first enzyme molecule that is extracted
from the DC by a rotor; kr(2)
~ 9,999 molecules/rotor-sec for the second molecule extracted; and
so forth. At the end of enzyme extraction, the last enzyme molecule
present in the DC represents a concentration of ~10-9
M (~5 ×10-10 molecules/nm3),
giving a final rotor rate kr(10,000
= nenz) ~ 1
molecule/rotor-sec for the last enzyme molecule that is extracted
from the DC by a rotor. The first molecule to be extracted takes (1/kr(1))
= 100 microsec for one rotor to extract, whereas the last molecule
to be extracted takes (1/kr(10,000
= nenz)) = 1 sec for a rotor
to extract. For the entire extraction process, the average number of
rotor-sec per molecule required to empty the DC of
nenz enzyme molecules
approximates the sum of the harmonic series (1/kr(1))
+ (1/kr(2)) + ... + (1/kr(nenz))
divided by the number of molecules, or krotor-1
~ (gamma + ln(nenz)) /
nenz = 0.978756 ×10-3
rotor-sec/molecule, where Euler's constant gamma ~ 0.577215... and
nenz >> 1. Hence the net
transport rate for all nenz
molecules is krotor ~
nenz / (gamma + ln(nenz))
~ 103 molecules/rotor-sec for nenz
= 104 enzyme molecules, and taking
textract = 50 millisec, then
nrotor = nenz
/ (textractkrotor)
= 200 rotors.

However, increasing nrotor
to 2000 rotors to provide tenfold redundancy, while holding
textract constant, reduces
the required krotor by a
factor of 10 -- e.g., to kr(10,000)
~ 0.1 molecule/rotor-sec. According to
Section 3.2.2
of Nanomedicine [1,
LINK],
the diffusion current to a rotor of face area 200 nm2
(equivalent circular radius ~8 nm), taking the enzyme diffusion
coefficient as ~7 ×10-11 m2/sec
at 37°C, is ~2 molecules/sec when the enzyme concentration is
10-9 M at the rotor/digesta interface as the last
enzyme molecule is being extracted. This is now more than an order
of magnitude larger than the kr(10,000)
~ 0.1 molecule/rotor-sec requirement, so enzyme rotors are operating
well within the diffusion limit for these devices. After extraction
of all enzymes, the rotors for that enzyme are stowed with the rotor
blank space exposed, thus protecting stored enzymes from contact
with a potentially degradative intrachamber environment.

Increasing nrotor
to 2000 rotors per enzyme species also permits the elimination of
enzyme storage tanks and associated support structures, because 2
×104 enzyme molecules can be stored in 2000 rotors each
having 10 enzyme receptor sites per rotor. If the rotors are turned
at 1 kHz, the entire enzyme inventory is injected into the DC in ~1
rotor rotation time, giving tinject
~ 1 millisec.

3.1.4.3 Summary of Digestion Systems

During each sub-subcycle, 104 enzyme
molecules are injected into the digestion chamber in
tinject ~ 1 millisec (Section
3.1.4.2.2). Enzymatic digestive action then commences, requiring
tenz ~ 50 millisec to go to
completion (Section
3.1.4.2.1). The 104 enzyme molecules are then
extracted from the DC and returned to the in-rotor reservoir in
textract ~ 50 millisec (Section
3.1.4.2.2). Total processing time per sub-subcycle is
tssc ~ 101 millisec, so one
complete microbivore digestion cycle comprising 240 sub-subcycles
requires ~24.24 sec.

There is one set of 2000 enzyme-transport rotors
for each of the 40 enzyme species transported, hence there are
80,000 enzyme-transport rotors protruding into the DC. These rotors
have a total face area of 16 micron2, somewhat more than
the ~10 micron2 cylindrical DC sidewall area, thus
require some slight rotor invagination into the DC volume. The
rotors occupy a total onboard volume of 0.4 micron3 with
an additional 0.1 micron3 allocated for drive mechanisms,
housings, and other rotor-related support, for a total 0.5 micron3
enzyme-transport rotor volume allocation. If the binding energy of
each enzyme receptor is ~240 zJ [1,
LINK],
then the total energy cost to eject 104 enzyme molecules
from their rotors is ~0.0024 pJ, representing a mean power
requirement of 2.4 pW when injection is performed over
tinject ~ 1 millisec. Rotor
drag power during extraction is negligible, so full-cycle power
consumption averages ~0.024 pW.

It is well-known that protein components of the
cell membrane are continually removed and replaced, with the
turnover rate in the unprotected cellular environment varying for
different proteins but averaging a half-life of ~200,000 sec or ~ 2
days [140,
141]. However, each enzyme spends a total time of 0.306 sec per
digestion cycle (Table
6) exposed to the morcellate or intermediate digesta, which
suggests useful enzyme suite lifetimes of at least 104-105
digestion cycles (e.g., mission lifetimes >3-30 days assuming
continuous digestive activity) conservatively may be expected. In
typical clinical deployments to combat acute bacteremia, each
microbivore will experience at most 1-10 digestion cycles during the
entire mission. Additionally, artificial enzymes that are deployed
in relatively nondegradative controlled intrananorobotic
environments might be expected to survive perhaps an order of
magnitude longer than natural enzymes in the wild. This increased
survivability, coupled with the tenfold redundancy of all critical
onboard systems including the artificial enzymes and their transport
mechanisms, suggests that extended microbivore missions lasting many
months in duration might be feasible.

3.1.4.4 Ejection Piston and Exhaust Port

Once microbial digestion is complete, the digesta
must be discharged into the external environment of the nanorobot.
Egestion is achieved using an annular-shaped ejection piston
comprised of a 20-nm thick piston pusher plate driven by at least
two 2-micron long, 10-nm thick pusher cables, comprising ~0.02
micron3 of device volume. This piston moves forward at
~200 micron/sec, applying ~0.1 atm of pressure to push digesta of
viscosity <1 kg/m-sec through a 1 micron2 gated annular
exhaust port, through a distance of the 2-micron DC length, emptying
the DC in ~10 millisec with a Poiseuille fluid flow power
dissipation [1,
LINK] of
~2 pW. Afterwards, the piston is retracted, effectively pulling a
vacuum in the DC in preparation to receive the next batch of
morcellate from the MC.

An annular exhaust port door must be opened prior
to activation of the ejection piston to allow the digesta to escape.
The exhaust port door is an oval-shaped irising mechanism [1,
LINK]
with an annular elliptical aperture measuring 0.721 microns × 1.227
microns along the inside curve and 1.108 microns × 1.884 microns
along the outside curve in vertical plane projection, providing a
1.161 micron2 aperture in the hull surface when fully
open. Assuming 0.5 micron2 of contact surfaces sliding ~1
micron at 1 cm/sec, power dissipation is ~3 pW during the 0.1
millisec door opening or closing time.

3.2 Microbivore Support Systems

Various mechanical subsystems are required to support
the principal activities of the microbivore digestive system. These
support subsystems include the power supply (Section
3.2.1), external and internal sensors (Section
3.2.2), the onboard computer (Section
3.2.3), structural support (Section
3.2.4), and a ballast system to permit nanapheresis (Section
3.2.5).

3.2.1 Power Supply and Fuel Buffer Tankage

The microbivore is scaled for a maximum power output
of 200 pW. The power source is assumed to be an efficient oxyglucose
powerplant such as a fuel cell, with net output power density of ~109
W/m3 [1,
LINK].
Each powerplant thus requires an onboard volume of 0.2 micron3.
Ten powerplants (each one independently capable of powering the
entire nanorobot at its maximum power requirement) are included
onboard for redundancy, giving a total powerplant volume requirement
of 2 micron3.

The microbivore is initially charged with glucose
and compressed oxygen (stored in sapphire-walled tankage), and
thereafter absorbs its ongoing requirements directly from the
bloodstream. Assuming 50% energy conversion efficiency and a 200 pW
continuous power production requirement, each glucose and oxygen
molecule that are consumed produce 2382.5 zJ or 397.1 zJ,
respectively [1,
LINK],
indicating a peak burn rate of 8.4 ×107 molecules/sec of
glucose and 50 ×107 molecules/sec of O2.

The minimum glucose concentration in normal adult
human blood is 2.3 ×10-3 molecules/nm3
[1,
LINK].
From Eqns.
3.4 and
4.7 in Nanomedicine
[1],
the required glucose current may be supplied by 13 receptor sites on
the device surface at the diffusion limit, assuming device radius ~1
micron and receptor radius ~1 nm. However, at the minimum
bloodstream concentration a conventional molecular sorting rotor
transports ~106 molecules/rotor-sec, so a minimum of 84
rotors are required to provide the required maximum flow. The
present design employs 100 glucose rotors for each of the ten
independent powerplants. A small number of glucose rotors could also
be positioned for uptake inside the digestion chamber, allowing the
scavenging of any microbe-derived glucose before the digesta is
expelled; however, this facility is not included in the current
design.

The minimum free molecular oxygen concentration in
normal adult human blood is 3.0 ×10-5
molecules/nm3 in venous blood and 7.3 ×10-5
molecules/nm3 in arterial blood [1,
LINK].
From Eqns.
3.4 and
4.7 in Nanomedicine
[1],
the required oxygen current may be supplied at the diffusion limit
by ~1200 receptor sites on the device surface, while in arterial
blood; by ~2000 receptor sites assuming an average 50%/50%
arterial/venous environment during one complete circulation; or by
~6200 receptor sites in venous blood alone. However, at blood plasma
oxygen concentrations a conventional molecular sorting rotor
transports ~105 molecules/rotor-sec, so a minimum of
~5000 rotors are required to provide the required maximum flow. The
present design employs 7500 oxygen rotors for each of the ten
independent powerplants, thus retaining full tenfold redundancy
throughout.

Waste products from oxyglucose power generation
include water and carbon dioxide. There are 50 ×107
molecules/sec of each waste species produced, which may be ejected
from the nanorobot using 500 standard sorting rotors for each
species, assuming a transport rate of ~106
molecules/rotor-sec. The present design thus employs 500 rotors each
for H2O and for CO2, for each of the ten
independent powerplants. However, in an emergency these wastes could
alternatively be bulk-vented to the external environment without
harmful effect -- the effervescence limit for point releases of bulk
CO2 in arterial plasma is ~70 ×107
molecules/sec [1,
LINK].

The microbivore design thus includes 86,000
small-molecule sorting rotors for energy-molecule transport with
full tenfold redundancy, occupying a total of ~8.6 micron2
of microbivore surface area and 0.103 micron3 of
microbivore volume. Energy dissipation by the rotor system, if
operated at the maximum 200 pW production rate, is 16 pW assuming
the transfer of 158.4 ×107 molecules/sec at an energy
cost of ~10 zJ/molecule (net energy cost after compression energy
recovery) [1,
LINK]. On
the microbivore surface, the energy-molecule transport rotors are
arranged as compactly as possible into ten lune-shaped sectors (one
for each of the ten powerplants) running from front to back (i.e.,
from ingestion port to exhaust port), with 8600 rotors/lune.

Diamondoid mechanical cables may transmit internal
mechanical energy at power densities of ~6 ×1012 W/m3
[1,
LINK].
Therefore a single cable that can transmit the entire microbivore
power output of 200 pW may have a volume of ~3 ×10-5
micron3, or ~5 ×10-5 micron3
including sheathing. To connect every powerplant with each of its 9
neighbors via power cables, permitting rapid load sharing among any
pair of powerplants inside the device, requires 45 power cables;
assuming 1000 internal power cables to accommodate additional power
distribution tasks and for redundancy, total power cable volume is
0.05 micron3. By varying the cable rotation rate, the
same power cables can simultaneously be used to convey necessary
internal operational information including sensor data traffic and
control signals from the computers.

3.2.2 Sensors

The microbivore needs a variety of external and
internal sensors to complete its tasks. External sensors include
chemical sensors for glucose, oxygen, carbon dioxide, and so forth,
up to 10 different molecular species with 100 sensors per molecular
species. Each 10 nm × 45 nm × 45 nm chemical concentration sensor
with 450 nm2 face area is assumed to discriminate
concentration differentials of ~10% and displace ~105 nm3
of internal nanorobot volume [1,
LINK].
Taking chemical sensor energy cost as ~10 zJ/count [1,
LINK]
with ~104 counts/reading [1,
LINK],
then 10 readings/sec by each of 1000 microbivore sensors gives a
maximum sensor power requirement of ~1 pW by a chemical sensor
facility that displaces a total of ~0.1 micron3 of device
volume and 0.45 micron2 of device surface area.

Acoustic communication sensors mounted within the
nanorobot hull permit the microbivore to receive external
instructions from the attending physician during the course of in
vivo activities. Assuming (21 nm)3 pressure transducers [2,
LINK], then 1000 of these transducers displace ~0.01 micron3
of device volume and 0.44 micron2 of device surface area,
producing a small net power input to the device of ~10-4
pW when driven by continuous 0.1-atm pulses [2,
LINK].

An internal temperature sensor capable of
detecting 0.3°C temperature change [1,
LINK] may
have a volume of (~46 nm)3 ~ 10-4
micron3; positioning ten such sensors near each of the 10
independent powerplants for redundancy implies a total internal
temperature sensor volume of ~0.01 micron3. An additional
0.03 micron3 of unspecified internal sensors are included
in the microbivore design, bringing the total for all sensors to
0.15 micron3.

3.2.3 Onboard Computers

Starting with Drexler's benchmark (400 nm)3
gigaflop mechanical nanocomputer [93],
the microbivore computer is scaled as a 0.01 micron3
device in principle capable of >100 megaflops but normally operated
at <~1 megaflop to hold power consumption to <~60 pW. Assuming ~5
bits/nm3 for nanomechanical data storage systems [93]
and a read/write cost of ~10 zJ/bit at a read/write speed of ~109
bits/sec [1,
LINK;
93], then 5 megabits of mass memory to hold the microbivore
control system (Table
4) displaces a volume of 0.001 micron3 and draws ~10
pW while in continuous operation. The current microbivore design
includes ten duplicate computer/memory systems for redundancy (with
only one of the ten computer/memory systems in active operation at a
time), displacing a total of 0.11 micron3 and consuming
<~70 pW.

3.2.4 Structural Support

The external microbivore hull is taken as a 50-nm
thick diamondoid surface of surface area 24.885 micron2
(again excluding the 2 micron2 of ports), a materials
volume of 1.2443 micron3. The buckling pressure of a
circular diamondoid cylinder of similar dimensions, subjected to
crushing forces, is ~300 atm. However, an ellipsoidal hull is
considerably weaker than a circular hull so some internal
cross-bracing (not included in the present design) might be
necessary to resist the ~50 atm force of dental grinding [1,
LINK;
2,
LINK].

An additional 0.3799 micron3 of
unspecified mechanisms and support structure are included in the
present design, which is summarized in
Table
5.

* Not all systems
are operated at peak power requirement simultaneously;
normal power usage is typically 50-150 pW.

3.2.5 Ballasting for Nanapheresis

As in previous designs [2,
LINK], the microbivore can alter its overall density to achieve
approximately neutral buoyancy, thus allowing convenient removal
from the patient's body via nanapheresis [1,
LINK]
after the therapeutic purpose is complete. (More elegant methods for
nanorobot ingress and egress from the human body are readily
imagined but are beyond the scope of this scaling design study.)
Density is altered by exhausting the onboard O2 buffer
tank and then pistoning the MC and DC empty, thus establishing a
vacuum in both chambers. If either or both of the pistons have
failed, the device can still be prepared for nanapheresis by venting
the compressed oxygen into the MC and DC, blowing the two chambers
clear of fluid and filling this volume with gas, which is
substantially similar in density to vacuum from the standpoint of
ballasting.

Assuming a mean density of 1900 kg/m3
for diamondoid nanomechanical structure, the "dry weight" of a
microbivore is ~12.2 pg, giving a minimum achievable density of
~1000 kg/m3. The density of a fully charged microbivore
with both chambers loaded is ~17.0 pg, a net density of ~1400 kg/m3.
The mean atomic weight per atom in simple nanomechanical system
designs available in 2001 [192,
LINK]
ranged from 7.5-18.8 daltons/atom of structure, with an average of
12 daltons/atom; taking the average figure, the microbivore consists
of 610 billion structural or permanent atoms, plus ~15 billion
molecules of oxygen when fully charged at 1000 atm and 135 billion
molecules of water (solvating 2.52 billion glucose molecules) with
both chambers flooded.

4.1 Phagocytic Activity of Microbivores

Table 6 shows the
approximate timeline for microbivore phagocytic activity during a
single, complete microbe digestion cycle. One microbivore can
completely digest one microbe that is up to ~2 microns3
in volume -- such as a P. aeruginosa bacterium -- in a time
tdigest ~ 30 seconds. This
is comparable to the 30-sec P. aeruginosa killing time of the
chlorine dioxide/ammonia-based industrial chemical sterilant
Cryocide [173]
or the chemical germicide hydrogen peroxide [174],
except that the microbivore also provides complete digestion of the
pathogen. (Intravenous LD50 of H2O2 in rats is
21 mg/kg [175].)
Larger microbes that are ~2-4 micron3 in volume could be
completely internalized in ~2.5 seconds by taking two quick "bites,"
although full digestion requires two complete cycles or ~60 seconds,
and still larger microbes could be ingested and digested piecemeal
at a continuous rate of ~4 micron3/nanorobot-min,
provided that some means can be found to avoid toxemia by ensuring
that the watertight seal of a partially fragmented organism grappled
against the nanorobot is maintained (possibly using flexible
lipophilic flaps or metamorphic bumpers [1,
LINK]). (Fungi
are larger than bacteria but replicate more slowly and are less
biotoxic, so the body's tolerance for material leakage during
piecemeal ingestion of these organisms should be greater.) The
microbivore consumes energy at a maximum rate of 200 pW, but more
typically operates at ~100 pW.

Natural phagocytic cells are 100-1000 times larger
in volume than microbivores but may consume almost as much power
during comparable activities. For example, heat production rises
from 9 pW in unstimulated human neutrophils up to 28 pW during
phagocytosis, with the rise proportional to the number of particles
ingested [176].
The basal rate for resting ~400 micron3 T-cell
lymphocytes is ~20 pW, rising to ~65 pW during antigen response [177,
178].

Microbe ingestion times for natural professional
phagocytes can be quite rapid, although complete digestion and
excretion of the target pathogen may require hours. For example,
13.8-micron diameter murine bone-marrow macrophages have been
observed ingesting a 15 micron particle in 30 minutes [179],
whereas an ~8-micron lymphocyte was ingested by a macrophage in only
3 minutes with dramatic shape changes, including formation of a
pseudopod 155 microns in length [180].
Nevertheless, while macrophages can ingest up to ~25% of their
volume per hour [105],
microbivores can process ~2000% of their volume per hour, thus are
about 80 times more efficient as phagocytic agents, in terms of
volume/sec digested per unit volume of phagocytic agent.

Natural professional phagocytic cells such as
neutrophils also have a maximum capacity for phagocytosis during
their short lifetime, typically a few hours in blood or a few days
in tissue. In one experiment [181],
1-100 S. aureus or S. faecalis bacteria were presented
to each neutrophil (PMN), which digested more of them at the higher
concentrations. At the highest concentration (100:1), PMNs from
normal patients could only kill a mean of 9 S. aureus
bacteria per PMN, while PMNs from carriers of of chronic
granulomatous disease could kill a mean of 14 S. faecalis
bacteria per PMN. By comparison, a single microbivore completely
digests ~3000 microbes/day of P. aeruginosa bacteria with no
well-defined maximum lifetime capacity for phagocytosis.

4.2 Microbivore Pharmacokinetics

To crudely quantify the activity of a specific dose
size of microbivores, a simple model of microbe-microbivore
interaction may be constructed as follows.

Consider a population of microbivores of
spherical-equivalent radius RMV
and number density nMV
(nanorobots/m3), and a second population of microbes of
spherical-equivalent radius Rbug
and number density nbug
(microbes/m3), simultaneously present in a fluid
compartment of volume Vfluid,
temperature Tfluid, and
viscosity efluid.
There are NMV = (nMVVfluid)
microbivores and Nbug = (nbugVfluid)
microbes initially present in the fluid compartment.

After some incremental thermal diffusion time
Dt each
microbe migrates one diameter away from its previous position in the
fluid. Any microbivore that is entirely present within a radius of (Rbug
+ 2RMV) of the center of the
microbe's new position will be in collision with the microbe, hence
the probability of collision is pcoll
~ (4/3) pnMV (Rbug
+ 2RMV)3 and the
half-life for microbe-microbivore collision is
t½ = Dt
ln(½) / ln(1-pcoll) where
Dt = 12
pefluidRbug3
/ kT
for an RMS displacement of one microbial diameter [1,
LINK].
The half-life for microbe removal is therefore
thalf = t½Ncoll,
where Ncoll is the number of
microbe-microbivore collisions required to ensure adhesion and
capture. That is, after a time thalf
has elapsed, the fixed population of microbivores has eliminated
half of the original population of target microbes. This formulation
assumes the usual therapeutic situation wherein a large surplus of
nanorobots is present relative to the target microbes (NMV
>> Nbug), in which case each
microbivore only rarely consumes more than a single microbe during
the therapeutic mission time tmission.
This formulation allows us to ignore the microbivore phagocytic time
tdigest ~ 30 sec (Section
4.1) as long as tmission
> tdigest.

However, microbes are not entirely passive targets
for nanorobotic digestion. After one microbial replication time
trepl
has elapsed, all extant microbes produce a single daughter microbe,
doubling the surviving population of microbes. The fastest known
bacterial replicators have a mean generation time of 900-1200 sec [182,
183]. In one experiment, E. coli and P. aeruginosa
replicating in the peritoneal cavities of mice having normal host
clearance mechanisms displayed generation times of 33 min (1980 sec)
and 20 min (1200 sec), respectively, during the first stages of
infection [184];
in another experiment P. aeruginosa had a doubling time of
30-32 min (1800-1920 sec) while replicating in normal mouse lung but
only 16 min (960 sec) in granulocytopenic (immune-compromised) mice
[185].
(Enterobacteria such as E. coli divide only once every 12-24
hours when in the human colon (i.e., trepl = 43,200-86,400
sec) [186],
far slower than the optimal laboratory batch rate of
trepl
~ 1000 sec.)

Similar bacteremias could be eliminated in 1.5 hr
(mild case) to 2.1 hr (severe case) using a 0.1 terabot dose if
Ncoll = 1, but the infection
cannot be controlled with only 1011 microbivores if
Ncoll = 10 because the
bacteria can replicate faster than the fixed microbivore population
can capture and digest them in this situation. The breakeven
microbivore dose that is just large enough to prevent the microbial
population from expanding, but is too small to reduce it, is
obtained by setting trepl
> ~ t½ and is given by:

for the variables as given above, as an
approximation when pcoll <<
1 as will normally hold for up to ~terabot doses of micron-sized
nanorobots. Interestingly, the effective nanorobot dosage is nearly
independent of the blood concentration of microbes as long as
NMV >>
Nbug, as was earlier presumed.

While microbivores can fully eliminate septicemic
infections in minutes to hours, natural phagocytic defenses -- even
when aided by antibiotics -- can sometimes require weeks or months
to achieve complete clearance of target bacteria from the
bloodstream (Section
2.1). Thus microbivores appear to be up to ~1000 times
faster-acting than either natural or antibiotic-assisted biological
phagocytic defenses. Only when the pathogens are seriously crippled
can the natural defenses achieve comparable clearance rates. For
example, in one experiment [187]
mice were able to clear ~80% of a 5000 CFU/gm dose of sialic
acid-deficient group B streptococci by phagocytosis within 1 hour,
whereas a like number of nondeficient streptococci similarly placed
evaded phagocytic killing and disseminated to various tissues.

Another useful comparative perspective is that the
administration of antibacterial agents (e.g., against E. coli)
typically may increase the LD50 of that pathogen by ~500-fold using
antibiotics [30]
or ~850-fold using monoclonal antibodies [188].
For example, the mammalian LD50 for E. coli is ~0.1-1 ×106
CFU/ml [27-30],
rising to ~108 CFU/ml with the administration of
antibiotics. By employing a suitable dose of microbivores, a
bloodstream bacterial concentration up to the theoretical maximum of
~1011 CFU/ml (~20% of blood volume assuming ~2 micron3
organisms) could be controlled, bringing another ~1000-fold
improvement using nanomedicine and at last extending the therapeutic
competence of the physician to the entire range of potential
bacterial threats, including locally dense infections.

For microbivores, several additional
biocompatibility issues also must be explicitly addressed. First,
nanorobots larger than ~1 micron in all three physical dimensions
are subject to possible
geometrical
trapping in the
fenestral slits of the splenic sinusoids in the
red pulp
of the spleen [192].
A small percentage of blood is forced to circulate through a
physical filter in the spleen requiring passage through slits
measuring 1-2 microns in width and ~6 microns in length [194-196].
Microbivores which become pinned to a slit face-on, or which become
stuck edge-on during an attempted passage, can detect that they have
become trapped by measuring various blood component concentration
and pressure differentials across their surfaces. The nanorobot then
activates its automatic
splenofenestral escape protocol, which involves the extension
and patterned ciliation of surface grapples until sensor readings
reveal that passage through the slit is complete, which is then
followed by grapple retraction.

Third, the careless internalization of motile
bacilli having long flagellar tails could result in the release of
truncated bacterial tails into the bloodstream (Section
3.1.3). The typical bacterial flagellum is a close-packed rigid
helix ~20 nm in diameter with a ~3 nm flagellin protein core, and
its length is almost always >100 times its thickness [199],
e.g., up to 10 microns long. There is significant antigenic
diversity among bacterial flagellar epitopes [200-205]
that white cells can recognize [206].
For example, Salmonella flagella are antigenically diverse
and highly immunopotent [201]
-- purified Salmonella typhi flagellar protein decreases CD14
expression and potently induces proinflammatory cytokine production
(e.g., TNF-alpha, IL-6, IL-10, gamma interferon) by human peripheral
blood mononuclear cells, and dramatically reduces expression of CD54
on macrophages, thus reducing the ability of those cells to take up
soluble antigen [207].
Free releases of bacterial flagella into the bloodstream could
produce inflammation or various immune system responses, thus should
be avoided. Complete internalization of tail may be ensured by
specialized operational routines (e.g., forced end-over-end rotation
of an internalized microbe while inside the MC, thus completely
spooling the tail into the microbivore before fully sealing the
ingestion port door), by specialized mechanical tools or jigs (e.g.,
a counterrotating interdigitated-knobbed capstan-roller pair, not
included in the present design), or by other means. The modulus of
rigidity for representative Salmonella flagellum has been
measured as ~1 ×1010 N/m2 [242];
from Eqn.
9.44 of Nanomedicine
[1],
the force required to buckle a 1-micron length of this flagellum is
~0.8 nN, far less than the ~100 nN force available from the MC
chopping blade (Section
3.1.3).

Another microbivore-specific
biocompatibility
issue derives from the onboard presence of active artificial
digestive enzymes. Although occurrences should be rare, stray intact
artificial enzymes could be missed by the extraction rotors or could
suffer some form of partial degradation and subsequently be egested
into the bloodstream. Such enzymes or enzyme fragments could exhibit
immunogenic, inflammatory, or other harmful activity in the body [208-212],
produce localized hyperenzymemia [213]
(often itself benign, as in hypertransaminasemia [214,
215]), or could serve as unintentional inflammatory mediators [216].
Fortunately, these artificial enzymes should prove quite fragile
outside of the relatively well-controlled and protective microbivore
internal environment, and should be rapidly attacked by natural
enzymes and quickly degraded to harmless peptides and amino acids.
Given a proper enzyme-transport system design, the release rate of
such molecules should be extremely low.

Finally, the current microbivore design has an
inherent minor iatrogenic vector vulnerability given that, in
principle, an artificial virus could be created that would bind only
to a region of the nanorobot surface that lies within the no-reach
radius of the grapple arms. Since adjacent grapples cannot reach
into this area either, a virus that affixes itself within the
no-reach circle closest to the base of each grapple could not easily
be dislodged mechanically. It may be possible to detect this
unwanted passenger by noticing that some rotors are blocked in a
particular area, but a forced reverse flow from blocked sorting
rotors probably would not be sufficient to dislodge such a bound
virion. In the case of a bloodborne virus, this is not a
particularly serious concern since the virus was in the bloodstream
anyway and little protection is conferred upon it simply by virtue
of its being permanently bonded to the microbivore hull. The
iatrogenic risk increases for more advanced microbivore-class
nanorobots that can crawl through tissues, or move from organ to
organ, or move between tissues and blood. This mobility creates a
potential danger of inadvertently spreading a viral infection from
one localized area to many other areas, should the virion
subsequently become detached. For these devices, either an
anti-blind-spot viral-removal protocol must be created and
implemented, or else the blind spot must be removed by: (1) adding
more angle links to the grapples, thus improving their reach; (2)
positioning grapple silos closer together so an adjacent grapple arm
can always reach into the blind spot; (3) adding specific virus
dislodgement mechanisms analogous to physical wiper blades or
localized jets of compressed gas at the base of every grapple silo;
or (4) by otherwise eliminating the blind spot.

4.4 Extended Applications

The present microbivore design has emphasized the
phagocytosis of isolated bloodborne bacterial pathogens. But
microbivores, as a general class of medical nanorobots, have much
broader applicability which can only briefly be summarized here.

4.4.1 Infections of Meninges and Cerebrospinal
Fluid

Microbivores could be useful in the treatment of
infections of the meninges and the cerebrospinal fluid (CSF). For
example, bacterial counts in the CSF of children [217]
and rhesus monkeys [218]
with Hemophilus influenzae meningitis can range from 102-109
CFU/ml, and 105-106 CFU/ml is sufficient to
produce inflammation [219].
Rabbit models show that a single intravenous ampicillin dose of
~0.125 gm (0.8 mg/ml blood) reduces H. influenzae bacteria in
CSF from 107 CFU/ml to 2.2 ×103 CFU/ml after 8
hours, a bacterial kill rate of 10-0.46
CFU/ml-hr [220].
A similar rabbit model involving E. coli meningitis found
bacterial kill rates of 10-0.88 CFU/ml-hr
for cefotaxime and 10-0.77 CFU/ml-hr for
pefloxacin at a dose rate of 0.5 mg/ml-hr [221].
The comparable bacterial kill rate for a similarly-sized single
0.01-terabot dose of microbivores delivered directly into the CSF
(~0.8 mg/ml) could similarly reduce the CSF bacterial count from 107
CFU/ml to 2.2 ×103 CFU/ml in ~540 sec (9 min)
optimistically assuming Ncoll
~ 1, is 10-24.4 CFU/ml-hr, a 53-fold
improvement over ampicillin.

4.4.2 Systemic Inflammatory Cytokine Management

With minor additions, microbivores could be used to
combat toxemia, the distribution throughout the body of poisonous
products of bacteria growing in a focal or local site, and other
biochemical sequelae of sepsis. For instance, E. coli-induced
septicemic shock in vervet monkeys occurred at 425 ×106
CFU/ml and LPS endotoxin rose from normal at 0.076 ng/ml to a
maximum of 1.130 ng/ml blood concentration [222].
In another study, endotoxin levels during a gram-negative bacterial
infection rose from 0.2 to 2 ng/ml in pig blood [223].
Eliminating a bloodstream concentration of ~2 ng/ml of ~8 kDa LPS
endotoxin [224]
would require the extraction and enzymatic digestion of ~8 × 1014
LPS molecules from the ~5400 cm3 human blood compartment,
a mere ~800 LPS molecules per nanorobot assuming a single terabot
dose (1012 devices) of modified microbivores.

The high mortality associated with gram-negative
sepsis is due in large measure to the patient's reaction to LPS,
which induces the production of cytokines such as IL-1beta and IL-6
which leads to an uncontrolled inflammatory reaction resulting in
tissue damage and organ failure [225].
Small quantities (~ng/ml) of LPS are released by living and growing
bacteria (see previous paragraph), but the killing of bacteria using
traditional antibiotic regimens often liberates large quantities of
additional LPS, potentially up to ~105 ng/ml [225].
Such massive releases as occur with the use of antibiotics will not
accompany the use of microbivores, because all bacterial components
(including all cell-wall LPS) are internalized and fully digested
into harmless nonantigenic molecules prior to discharge from the
device. Microbivores thus represent a complete antimicrobial therapy
without increasing the risk of sepsis or septic shock. (Note that
while gram-positive organisms can also induce cytokine production,
100- to 1000-fold more gram-positive bacteria are needed to induce
the same concentration of cytokines as are induced by gram-negative
bacteria [225].)

If the patient presents with a septic condition
before the microbivores are introduced, a substantial preexisting
concentration of inflammatory cytokines will likely be present and
must be extracted from the blood in concert with the principal
antibacterial microbivore treatment. All unwanted cytokine molecules
may be rapidly and systemically extracted from the blood using a
modest dose of respirocyte-class nanodevices [2,
LINK], a combination-treatment approach previously suggested
elsewhere [1,
LINK;
191,
LINK]. Specifically, a 1-terabot intravenous dose of micron-size
pharmacytes [1,
LINK,
LINK]
each having ~105 cytokine-specific molecular sorting
rotors and ~0.5 micron3 of onboard storage capacity could
reduce the blood concentration of ~20 kDa IL-1beta and IL-6
cytokines from LPS-elevated levels of ~100 ng/ml [225]
(~3 ×10-9 molecules/nm3) down to
normal serum levels of ~10 pg/ml [226]
(~3 ×10-13 molecules/nm3) after
only ~200 sec of diffusion-limited pumping, using just ~0.1% of the
available onboard storage volume. (Extracting an additional ~105
ng/ml of LPS from the bloodstream would take a similar amount of
time and would use ~100% of the available onboard storage volume.)

A temporary sequestration of iron from the blood,
mimicking the effect of lactoferrin released by natural phagocytes,
could further enhance microbivore effectiveness by slowing the
bacterial growth rate and increasing trepl.

4.4.3 Biofilm Digestion

Microbivores, slightly altered, could also be used to
digest bacterial biofilms [227].
Biofilms may vary widely in thickness, which is limited more by
nutrient transport than by surface roughness. In vitro experiments
show that aerobic Pseudomonas aeruginosa biofilms can grow to
30-40 microns in depth as monocultures, but may increase in depth to
130 microns when the culture is amended with anaerobic bacteria [228].
Microbivores can digest biomaterial at a rate of ~4 micron3/min,
hence an array of closely packed microbivores (~6.8 micron2/device)
attached to a biofilm can consume the biofilm at a rate of ~10
nm/sec, requiring ~105 sec (~3 hr) to consume an entire
100-micron thick biofilm. Again, some means must be found to ensure
a watertight seal between partially fragmented organisms and the
microbivore ingestion port (Section
4.1).

4.4.4 Bacterial Infections in Other Fluids and
Tissues

Bacteria present in sputum or in the mucous layers of
the throat may be pursued by somewhat larger ambulatory microbivores
having an additional array of longer grapples that could serve as
locomotive mechanisms (legs), thus permitting the nanorobots to
engage in microbial search-and-destroy missions along the luminal
surfaces of the human trachea, bronchi, and bronchioles [229].
Normally there may be ~105 CFU/ml bacteria colonizing the
oropharynx [230],
>107 CFU/ml in sputum or throat swab during respiratory
infections [231]
or cystic fibrosis [232],
and sputum infections up to ~4 ×108 CFU/ml have been
reported [233,
234].

4.4.5 Viral, Fungal, and Parasitic Infections

Microbivores can rid the blood of viral pathogens,
which are typically present during viremia at concentrations similar
to those found in bacteremia, ~0.1-100 ×106/ml (Section
2.2). Viruses tend to be much smaller than most bacteria, so
processing time per virion may be considerably reduced, perhaps 5-10
seconds or less. Apparently the human body is already fairly
efficient at removing virus particles from the bloodstream -- for
instance, in one study of HIV-1 infected patients, measurements of
plasma virus loads found that individual virions had a clearance
half-life of 28-100 min for HIV-1 and 100-182 min for hepatitis C
(HCV) virus [239].
The difficulty for the natural defensive systems is that replacement
viruses are rapidly replicated and discharged into the blood by
infected cells, thus perpetuating the infection. For example, the
daily particle production rate in HIV-1 infected patients has been
estimated as 2-16 ×109 particles/day for HIV-1 and 0.4-10
×1012 particles/day for HCV [239].
Such production rates are nevertheless easily controlled by a
terabot population of microbivores which has a collective digestive
capacity of >1015 virions/day. One additional
complication, well within the competence of the the current
microbivore design, is that some viruses like HIV are mutating
constantly, so that one patient may have as many as 8-10 different
strains concurrently, all of which must be successfully recognized
and eliminated.

Fungemias involving particle loads of 1-1000
CFU/ml (Section
2.3) are rapidly cleared by microbivores. Fungal particles may
be up to ~400 micron3 in volume, requiring ~100 min for
complete digestion using a microbivorous protocol that employs
careful piecewise digestion involving ~800 "bites" (Section
4.1). Blood parasites of comparable size (Section
2.4) may be present at concentrations similar to those found in
bacteremia but may be controlled with terabot doses of microbivores.

4.4.6 Other Applications

Microbivores could be designed to trap and retain
(without digesting) samples of unknown microbes found floating in
the bloodstream, when those microbes fall within a certain
physician-specified size range and are confirmed not to be platelets
or chylomicrons. These samples could then be returned to the
attending physician for further investigation, following
nanapheresis. Ranging still further afield, microbivore-derived
devices could be employed in veterinary and military applications;
to disinfect surfaces, objects, and volumes (e.g., 102-105
CFU/ml bacteria found in the sink fluid of washbasin drains in a
pediatric ward [240])
or to sterilize organic samples or edible foodstuffs; to clean up
biohazards, biopolluted drinking water, toxic biochemicals, or other
environmental organic materials spills, as in bioremediation; and in
many other useful applications.

5. Conclusions

This paper presents a theoretical nanorobot scaling
study for artificial mechanical phagocytes of microscopic size,
called "microbivores," whose primary function is to destroy
microbiological pathogens found in the human bloodstream using a
digest and discharge protocol. Some
images of microbivores are now available online.

The microbivore is an oblate spheroidal
nanomedical device measuring 3.4 microns in diameter along its major
axis and 2.00 microns in diameter along its minor axis, consisting
of 610 billion precisely arranged structural atoms in a gross
geometric volume of 12.1 micron3. During each cycle of
operation, the target bacterium is bound to the surface of the
microbivore via species-specific reversible binding sites.
Telescoping robotic grapples emerge from silos in the device
surface, establish secure anchorage to the microbe's plasma
membrane, then transport the pathogen to the ingestion port at the
front of the device where the cell is internalized into a
morcellation chamber. After sufficient mechanical mincing, the
morcellated remains are pistoned into a digestion chamber where a
preprogrammed sequence of engineered enzymes are successively
injected and extracted, reducing the morcellate primarily to
monoresidue amino acids, mononucleotides, glycerol, free fatty acids
and simple sugars, which are then harmlessly discharged into the
environment, completing the cycle.

The device may consume up to 200 pW of continuous
power while completely digesting trapped microbes at a maximum
throughput of 2 micron3 of organic material per 30-second
cycle. Microbivores are up to ~1000 times faster-acting than either
natural or antibiotic-assisted biological phagocytic defenses, and
are ~80 times more efficient as phagocytic agents than macrophages,
in terms of volume/sec digested per unit volume of phagocytic agent.
Besides intravenous bacterial scavenging, microbivores or related
devices may also be used to help clear respiratory, urinary, or
cerebrospinal bacterial infections; eliminate bacterial toxemias and
biofilms; eradicate viral, fungal, and parasitic infections;
disinfect surfaces, foodstuffs, or organic samples; and help clean
up biohazards and toxic chemicals.

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